where \(F({1\over 2},{1\over 2},1,\lambda )=\sum _{n=0}^\infty {-1/2\atopwithdelims ()n}^2\lambda ^n\)  is a hypergeometric function. Note that for real \(\lambda \)  in the region the second period is real positive whereas the first is purely imaginary; the possibility of choosing such periods depends (as is not difficult to prove) on the fact that the real points of the corresponding elliptic curve have two components. We have the formulae ([1]}, Ch. 9, Thm. 6.1)
\(\omega _1(\lambda )=\int _{-\infty }^0{{\rm d}x\over y}\in i{R}, \qquad \omega _2(\lambda )=\int _1^\infty {{\rm d}x\over y}\in {R},\) 
